On the existence and structure of inhomogeneous analogs of the Dedekind and Jacobi ellipsoids

Details On the existence and structure of inhomogeneous analogs of the Dedekind and Jacobi ellipsoids On the existence and structure of inhomogeneous analogs of the Dedekind and Jacobi ellipsoids

Nov 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...250..362i&link_type=abstract

Astrophysical Journal, Part 1, vol. 250, Nov. 1, 1981, p. 362-372.

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34

Ellipsoids, Existence Theorems, Gravitational Fields, Rotating Fluids, Stellar Rotation, Astrodynamics, Equilibrium

Scientific paper

The existence and structure of fully nonaxisymmetric configurations of rapidly rotating inhomogeneous fluid bodies in gravitational equilibrium are investigated. A vector-pointing formalism is established for describing equilibrium configurations of inviscid fluid obeying a barotropic equation of state in which the density is constant along velocity streamlines, and used to investigate the existence of inhomogeneous Dedekind ellipsoids, in which a stationary surface is maintained in the inertial frame by internal motions with constant vorticity parallel to the shortest axis, and Jacobi ellipsoids, which rotate uniformly. A numerical method is used to construct Jacobi configurations with polytropic equations of state, demonstrating the existence of fully nonaxisymmetrical inhomogeneous equilibrium figures. In agreement with other analyses, however, calculations indicate that the Jacobi configurations do not exist for polytropic indexes greater than or equal to 0.8, and hence the Dedekind configurations do not exist at all, at least when the density vanishes at the surface.

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